Kits for interconnecting cylindrical tubes

ABSTRACT

A kit for joining cylindrical tubes to form strong orthogonally joints for use in a variety of structures comprises a tool for modifying the cylindrical tubes to demonstrate cutouts of specified width and depth, a Steinmetz solid connector having a shape defined by the volume of intersection of the two cylindrical volumes of equal diameter joined orthogonally; and an adhesive means for securing said connector within said cylindrical tubes. Kits that comprise one-, two-, and four-piece Steinmetz solid connectors are described, as are alternative means and members to secure and shape the resulting joint.

CROSS-REFERENCE TO RELATED APPLICATIONS

This U.S. Non-Provisional Utility Patent Application is a divisional ofU.S. Non-Provisional patent application Ser. No. 16/813,409, filed Mar.9, 2020, issued as U.S. Pat. No. 10,948,118 on Mar. 16, 2021 which, inturn, claims the benefit under 35 U.S.C. § 119 of U.S. ProvisionalPatent Application Ser. No. 62/817,588, filed Mar. 13, 2019, both by thepresent inventor, the contents of which are incorporated herein in theirentireties.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

The invention described herein was not made pursuant to a governmentagency grant or contract. No government funds were utilized in thedescribed invention.

FIELD OF THE INVENTION

The present invention is in the technical field of structural joints.More particularly, the present invention describes kits for joiningcylindrical tubes orthogonally.

BACKGROUND OF THE INVENTION

Cylindrical tubes are often joined orthogonally, in particular toprovide structural support for larger structures.

The most common methods of orthogonally joining two cylindrical tubesinvolves severing or separating each tube into two segments beforejoining the segments using an insert or socket connector.

Because each tube is separated in order to be joined, the structuralintegrity of the joint is significantly reduced. In order to restoresome structural strength to the joint, permanent adhesives are commonlyemployed to bind the tube segments to the connector. Additionally, tubesegments and connectors are often threaded to improve structuralstrength.

One object of the instant invention is to provide a method for joiningcylindrical tubes orthogonally without separating each tube intosegments before joining. By minimizing the structural modifications toeach tube, the remaining inherent structural integrity of the materialsis preserved.

A further object of the instant invention is a method of connectingcylindrical tubes orthogonally, employing a connector that maximizes theeffective contact surface area of the two tubes, thereby improving thestructural integrity of the joint.

A further object of the instant invention is a method for reversiblyjoining cylindrical tubes in a manner that does not significantly reducethe structural integrity of the resulting joint.

Still a further object of the instant invention is a method forreversibly joining cylindrical tubes orthogonally that allows for quickand efficient assembly/disassembly as well as modularity.

A further object of the instant invention is to produce an orthogonaljoint of modern aesthetic, in which surfaces between joint segments lieflush and transition smoothly.

Yet a further object of the instant invention is to provide apparatus ofcylindrical tubes joined by means of a Steinmetz solid connector.

Still another object of the instant invention is to provide a kitcomprising materials and tools to practice the described methods andconstruct the described apparatus.

SUMMARY OF THE INVENTION

These and other objects are accomplished in the present invention: kitswhich provide requisite tools and materials for performing the methodsfor orthogonally joining cylindrical tubes described herein.

A method of the instant invention comprises the following or equivalentsteps: (1) providing two cylindrical tubes of equal internal diameter;(2) modifying each tube to demonstrate a cutout at the location of theintended joint; (3) providing a connector in the shape of a bicylinderSteinmetz solid sized for the internal diameter; (4) joining themodified tubes around the connector with tubes aligned orthogonally,cutouts facing one another, and the interior surface of the tubesexposed by the cutouts abutting the surfaces of the connector. The tubescan be joined to one another through permanent adhesion or temporaryfastening to form the final assembly.

According to one embodiment of the method, the Steinmetz solid connectorcomprises a single piece.

According to another embodiment of the method, the Steinmetz solidconnector comprises two identical halves each of which is joined withone modified tube to create a half-connector/tube assembly. According tofurther embodiment of the method, the Steinmetz solid connectorcomprises four identical quarters, two of which are joined to each oneof the modified tubes to create a two quarter-connector/tube assembly.

According to yet additional embodiments of the method of the subjectinvention, the modified tubes joined by one of the Steinmetz solidconnector embodiments are optionally combined with one or more of thefollowing auxiliary parts: (1) stabilizing covers; (2) circular discs;(3) stepped stoppers; and (4) cutout bridges. These auxiliary parts arealigned and affixed to the modified tubes such that the final jointassembly demonstrates additional strength and smooth transitions.

The apparatus of the instant invention comprises two modifiedcylindrical tubes joined orthogonally and internally reinforced with aSteinmetz solid connector having a shape defined by the volume ofintersection of the hollow regions of the tubes when their cylindricalaxes intersect orthogonally.

The kit of the instant invention comprises a combination of one or moreof the following components: a tool for modifying cylindrical tubes withcutouts of specified width and depth, a Steinmetz solid connector havinga shape defined by the volume of intersection of cylindrical volumes ofspecified equal diameter and orthogonally intersecting cylindrical axes,adhesive for attaching the cylindrical tubes and connector, a strap foroptionally securing the joint in a releasable fashion, four stabilizingcovers, two or four circular discs, two stepped stoppers, and cutoutbridge.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of one embodiment of a first tube modifiedaccording to the second step of a method of the subject invention.

FIG. 2 is a side view of the first tube shown in FIG. 1 modifiedaccording to the second step of a method of the subject invention.

FIG. 3A is a perspective view of one embodiment of the Steinmetz solidshaped connector used in the third step of the method of the subjectinvention.

FIG. 3B is a perspective view of the Steinmetz solid shaped connectorshown in FIG. 3A inserted and affixed to the inside surface of the firsttube in accordance with the fourth step of a method of the subjectinvention.

FIG. 4A is a perspective view of another embodiment of the Steinmetzsolid shaped connector divided into two pieces identical in shape andsize.

FIG. 4B is a perspective view of one of the Steinmetz solid pieces shownin FIG. 4A inserted and affixed to the interior surface of the firsttube in accordance with the fourth step of a method of the subjectinvention.

FIG. 5A is a perspective view of another preferred embodiment of theSteinmetz solid connector divided into four pieces identical in shapeand size.

FIG. 5B is a perspective view of two of the Steinmetz solid pieces shownin FIG. 5A inserted and affixed to the interior surface of the firsttube in accordance with the fourth step of a method of the subjectinvention with the optional circular discs utilized.

FIG. 6 is a perspective view of the resulting joint created by a methodof the subject invention.

FIG. 7 is a perspective view of a releasable joint with optionalcrisscrossing straps created by preferred embodiment using a method ofthe subject invention.

FIG. 8A is a perspective view of a modified first tube with optionalstabilizing covers of the subject invention.

FIG. 8B is a perspective view of a modified second tube with optionalstabilizing covers of the subject invention.

FIG. 8C is a perspective view of the resulting joint created by a methodof the subject invention with the optional stabilizing covers utilized.

FIG. 9A is a perspective view of the optional stabilizing cover.

FIG. 9B is another perspective view of the optional stabilizing cover.

FIG. 10 is a perspective view of the optional circular discs of thepresent invention.

FIG. 11A is a perspective view of another embodiment of the first tubemodified according to the second step of a method of the subjectinvention.

FIG. 11B is a perspective view of another embodiment of the second tubemodified according to the second step of a method of the subjectinvention.

FIG. 12A is a side view of the first tube shown in FIG. 11A modifiedaccording to the second step of a method of the subject invention.

FIG. 12B is a side view of the first tube shown in FIG. 11B modifiedaccording to the second step of a method of the subject invention.

FIG. 13A is a perspective view of the optional cutout bridge of thesubject invention.

FIG. 13B is a perspective view of the optional cutout bridge affixed tothe smaller tube.

FIG. 14A is a perspective view of a resulting joint created by a methodof the subject invention with the optional cutout bridge utilized.

FIG. 14B is another perspective view of a resulting joint created by amethod of the subject invention with the optional stabilizing coversutilized.

FIG. 15A is a perspective view of the optional stepped stopper.

FIG. 15B is a perspective view of the optional stepped stopper insertedinto the smaller tube.

DETAILED DESCRIPTION OF THE INVENTION

The method of the instant invention comprises the following orequivalent steps: (1) providing two cylindrical tubes of equal internaldiameters, (2) modifying each tube at the location of the intended jointwith a cutout that exposes the interior surface of each tube; (3)providing a connector in the shape of a bicylinder Steinmetz solid sizedfor the internal diameter of the tubes; (4) joining the modified tubesaround the connector with the tubes aligned orthogonally, cutouts facingone another, and the interior surface of the tube exposed by the cutoutabutting the surfaces of the connector.

The method for connecting two tubes of the present invention begins withthe first step of providing two cylindrical tubes 1 a and 1 b. In thepreferred embodiment of the subject invention, selected tubes 1 a and 1b are both similar to the tube 1 a shown in FIG. 1. Tubes 1 a and 1 bare right circular hollow cylinders, which are a three-dimensionalregion bounded by an interior right circular cylinder 3 and exteriorright circular cylinder 5 having the same central axis 7 and twoparallel annular bases 9 a and 9 b perpendicular to central axis 7. Theinterior diameter 13 of the interior cylinders 3 for both tubes 1 a and1 b are equal in length. In a preferred embodiment of the subjectinvention, the exterior diameter 15 of exterior right cylinder 5 forboth tubes 1 a and 1 b are also equal in length.

The second step for method for connecting two cylindrical tubes 1 a and1 b of the present invention is modifying first and second tubes 1 a and1 b to demonstrate a cutout 12 of identical dimension on each tube withcutout 12 on each tube centered at the location of the intended joint.FIG. 1 is a perspective view of first tube 1 a having cutout 12.

FIG. 2 is a side view of tube 1 a shown in FIG. 1 after the second stepof a method of the subject invention. Referring to FIG. 2, the cutoutwidth 20 of cutout 12 is equal to the length of exterior diameter 15 andthe cutout depth 23 of cutout 12 is half the length of exterior diameter15. Once tubes 1 a and 1 b are modified with cutouts 12, each cutout 12creates two exposed half-circular cross sections 17 a and 17 b (shown inFIG. 1) that are perpendicular to central axis 7 at either side ofcutout 12.

After tubes 1 a and 1 b are modified to demonstrate cutouts 12 at thelocation of the intended joint, the next step of the method forconnecting tubes 1 a and 1 b of the subject invention is providing aconnector in the shape of a Steinmetz solid. FIG. 3A is a perspectiveview of the Steinmetz solid connector 30. A Steinmetz solid is a solidbody generated by the orthogonal (right-angle) intersection of two ormore cylinders of equal radius, whose axis of rotational symmetryintersect at the same point. In the case where two cylinders intersect,the overlapping space is called a “bicylinder Steinmetz solid” or atetragonal hosohedron. The subject invention concerns connector 30 ofthe bicylinder Steinmetz solid variant, where the radius of the twointersecting cylinders that create the bicylinder Steinmetz solid areequal to the length of interior diameter 13 of tubes 1 a and 1 b. Allreferences to a Steinmetz solid herein refer to the bicylinder Steinmetzsolid. The horizontal cross-section of connector 30 is a square with thelength of each side equal to interior diameter 13 of tubes 1 a and 1 b.In other preferred embodiments, connector 30 can be divided into two ormore pieces.

In the preferred embodiment shown in FIG. 4A, connector 30 is furtherdivided into two or more pieces such that when the pieces are arrangedand placed together, the pieces form a Steinmetz solid. Referring to thepreferred embodiment shown in FIG. 4A, connector 30 comprises of twoSteinmetz solid halves—40 a and 40 b—which are equal in shape and size,and when placed together, as shown in FIG. 4A, creates a Steinmetz solidshape of connector 30. Steinmetz solid halves 40 a and 40 b are the twopieces resulting from dividing the Steinmetz solid connector 30 alongcross section 33 shown in FIG. 3A.

In another preferred embodiment shown in FIG. 5A, connector 30 isdivided into four Steinmetz quarters, 52 a, 52 b, 52 c, 52 d, which areequal in shape and size, and when placed together creates the Steinmetzsolid shape. FIG. 5A is a perspective view of the four Steinmetz solidquarters 52 a, 52 b, 52 c, and 52 d positioned together to form aSteinmetz solid connector 30. Steinmetz solid quarters 52 a, 52 b, 52 c,and 52 d are the four pieces resulting from dividing the Steinmetz solidconnector 30 shown in FIG. 3A along cross sections 33 and 35.

Connector 30, halves 40 a and 40 b, and quarters 52 a, 52 b, 52 c, and52 d can be fabricated by any means known in the art such asthree-dimensional printing.

The fourth step of the method of the present invention is joining tubes1 a and 1 b around connector 30 such that tubes 1 a and 1 b are alignedorthogonally with cutouts 12 facing one another and the interior surfaceof tubes 1 a and 1 b that were exposed by cutout 12 abutting against thesurfaces of connector 30. FIG. 6 is a perspective view of resultingjoint 60 formed by orthogonally aligning tubes 1 a and 1 b using amethod of the present invention.

In the embodiment where Steinmetz solid connector 30 is a single unit,as shown in FIG. 3A, connector 30 is inserted into first tube 1 athrough first cutout 12 and the surface of connector 30 that abuts withthe inside surface of the first tube 1 a that is exposed by cutout 12 isaffixed to the inside surface of first tube 1 a through the use of anepoxy, glue, adhesive, or any other means for affixing objects together.FIG. 3B is a perspective view of connector 30 inserted into first tube 1a demonstrating first cutout 12 that will accept second tube 1 b with anequal external diameter as first tube 1 b.

Second tube 1 b is positioned so that cutout 12 on tube 1 b faces cutout12 of first tube 1 a and first tube 1 a is orthogonal in position withrelation to second tube 1 b and the surface of connector 30 that abutswith the inside surface of second tube 1 b is affixed to the insidesurface of second tube 1 b that is exposed by cutout 12 creating joint60 shown in FIG. 6. Inside surface of second tube 1 b is affixed to thesurface of connector 30 using an epoxy, glue, adhesive or any othermeans for affixing objects together.

In the embodiments where connector 30 comprise more than one piece, eachpiece is attached to the interior surface of either one of two tubes 1 aand 1 b. Ideally half the pieces, but at least one piece, are affixed tothe interior surface of each tube 1 a and 1 b, and the pieces arearranged in such a way that when tubes 1 a and 1 b are alignedorthogonally with cutouts 12 on tubes 1 a and 1 b facing one another,the pieces form connector 30 having a Steinmetz solid shape.

According to the preferred embodiment wherein the Steinmetz solidcomprises two pieces of identical shape and size, connector 30 isbisected along a line connecting opposed corners of connector 30 tocreate connector halves 40 a and 40 b as shown in FIG. 4A. Eachconnector half 40 a and 40 b demonstrate a planar surface at the pointof bisection. According to method of this embodiment, first half 40 a isinserted into first tube 1 a through cutout 12 and the surface of firsthalf 40 a that abuts the interior surface of first tube 1 a is affixedto the interior surface of first tube 1 a that is exposed by cutout 12through the use of an epoxy, glue, adhesive, or any other means foraffixing objects together. Second half 40 b is inserted into second tube1 b through cutout 12 and the surface of second half 40 b that abuts theinterior surface of second tube 1 b is affixed to the interior surfaceof second tube 1 b that is exposed by cutout 12 through the use of anepoxy, glue, adhesive, or any other means for affixing objects together.

In a preferred embodiment shown in FIG. 4B, first tube 1 a shown in FIG.1 is modified to demonstrate cutout 12 that will accept second tube 1 bwith equal external diameter as first tube 1 a. First half 40 a isinserted into first tube 1 a and the surface of first half 40 a thatabuts with the interior surface of first tube 1 a is affixed to theinterior surface of first tube 1 a that is exposed by cutout 12.

Similarly, second tube 1 b is modified to demonstrate cutout 12 thatwill accept first tube 1 a with an equal diameter as second tube 1 b.Second half 40 b is inserted into second tube 1 b and the surface ofsecond half 40 b that abuts with the interior surface of second tube 1 bis affixed to the interior surface of second tube 1 b that is exposed bycutout 12. Halves 40 a and 40 b are arranged such that when tubes 1 aand 1 b are placed in the orthogonal position, with the planar surfacescreated by the bisection of connector 30 facing one another, halves 40 aand 40 b create the Steinmetz solid shape.

In this preferred embodiment, one method of ensuring that halves 40 aand 40 b will be arranged correctly once tubes 1 a and 1 b are alignedorthogonally is to arrange and insert both halves 40 a and 40 b intofirst tube 1 a so that it forms Steinmetz solid connector 30, attachingonly first half 40 a to the inside of surface tube 1 a, and thenremoving second half 40 b when the epoxy, adhesive, or other means foraffixing has set. The same method can then be done to second tube 1 b byarranging and inserting half 40 b and another half identical to 40 ainto second tube 1 b so that the arrangement forms Steinmetz solidconnector 30, attaching only half 40 b to the inside surface of tube 1 band removing the additional piece identical to half 40 a once the epoxy,adhesive, or other means for affixing has set. When the externaldiameters of tubes 1 a and 1 b are equal, the result will be two tubeswith the arrangement shown in FIG. 4B.

In the preferred embodiment where connector 30 is divided into fourquarters 52 a, 52 b, 52 c, and 52 d, as shown in FIG. 5A, quarters 52 aand 52 c are inserted into first tube 1 a through cutout 12 and thesurfaces of quarters 52 a and 52 c that abuts the interior surface offirst tube 1 a are affixed to the interior surface of first tube 1 athat is exposed by cutout 12 through the use of an epoxy, glue,adhesive, or any other means for affixing objects together. Quarters 52b and 52 d are inserted into second tube 1 b through cutout 12 and thesurfaces of quarters 52 b and 52 d that abut the interior surface ofsecond tube 1 b is affixed to the interior surface of second tube 1 bthat is exposed by cutout 12 through the use of an epoxy, glue,adhesive, or any other means for affixing objects together.

In a preferred embodiment shown in FIG. 5B, after first tube 1 a ismodified to demonstrate first cutout 12 that will accept second tube 1b, quarters 52 a and 52 c inserted into first tube 1 a with the exteriorsurfaces of quarters 52 a and 52 c that abut with the interior surfaceof first tube 1 a are affixed to the interior surface of first tube 1 a.

Similarly, second tube 1 b is modified to demonstrate second cutout 12that will accept first tube 1 a. Quarters 52 b and 52 d are insertedinto second tube 1 b with the exterior surface of quarters 52 b and 52 dthat abut with the interior surface of second tube 1 b is affixed to theinterior surface of second tube 1 b. Quarters 52 a, 52 b, 52 c, and 52 dare arranged such that when tubes 1 a and 1 b are placed in theorthogonal position quarters 52 a, 52 b, 53 c, and 53 d create theSteinmetz solid shape.

In this preferred embodiment, one method of ensuring that quarters 52 a,52 b, 52 c, and 52 d will be arranged correctly once tubes 1 a and 1 bare aligned orthogonally is to arrange and insert quarters 52 a, 52 b,53 c, and 53 d into first tube 1 a so that it forms Steinmetz solidconnector 30, attaching only first quarters 52 a and 52 c to the insideof surface tube 1 a, and then removing quarters 52 b and 52 d when theepoxy, adhesive, or other means for affixing has set. The same methodcan then done to second tube 1 b by arranging and inserting quarters 52b and 52 d and two quarter pieces identical to 52 a and 52 c into secondtube 1 b so that it forms Steinmetz solid connector 30, attaching onlyquarters 52 b and 52 d to the inside surface of tube 1 b and removingthe additional pieces identical to quarters 52 a and 52 c once theepoxy, adhesive, or other means for affixing has set. The result will betwo tubes with the arrangement of quarter pieces shown in FIG. 5B.

In the preferred embodiments where connector 30 is divided into two ormore pieces and the surface of each piece of connector 30 is onlyaffixed to one of the two tubes 1 a and 1 b, the resulting joint 60 isreleasable and temporary, such that joint 60 can be assembled and thenat a later time disassembled. In these preferred embodiments, tubes 1 aand 1 b are aligned orthogonally with cutouts 12 of tubes 1 a and 1 bfacing one another and the interlocking pieces align to form connector30.

In order to make joint 60 more secure, joint 60 can also be securedtogether with a means for securing such as using crisscrossing straps 72a and 72 b. In the preferred embodiment straps 72 a and 72 b are madewith hook and loop material, but any material used for strapping and/orsecuring can be used. FIG. 7 is a perspective view of joint 60 that isreleasable in the fully assembled state that is secured by twocrisscrossing hook and loop straps 72 a and 72 b.

Alternatively, if the surfaces of each piece that abuts with anotherpiece is affixed together and/or the surfaces of each piece that abutsthe interior surface of tube 1 a or 1 b are affixed together with theuse of an epoxy, glue, adhesive, or other means for affixing, joint 60becomes a fixed joint that is not releasable.

When the tubes 1 a and 1 b are fitted together orthogonally using themethod of the subject invention, crescent-shaped openings are apparentat each side of the cutout, creating a total of four crescent-shapedopenings. One of these crescent shaped openings 65 can be seen in FIG.6. These crescent-shaped openings allow water, sand, dust, lint, andother objects to enter the joint and the adjacent tubing and diminishthe aesthetic appearance of the joint.

Consequently, a further refinement of the invention includes attachingoptional stabilizing covers to cover each of the crescent shapedopenings 65 after the completion of the first step of theabove-described method of the subject invention. In addition to makingjoint 60 waterproof or water resistant and more aesthetically pleasingin appearance, the stabilizing covers also help stabilize joint 60 byadding rigidity to the connection of joint 60. When exterior diameters15 of tubes 1 a and 1 b are equal, four stabilizing covers 82 a, 82 b,82 c, and 82 d can be used.

Stabilizing covers 82 a, 82 b, 82 c, and 82 d always appear in pairs andare attached on opposite sides of cutouts 12 of tubes 1 a and 1 b usingepoxy, glue, adhesive, or any other means for affixing objects together.FIG. 8A is a perspective view of first tube 1 a after the second step ofa method of the present invention with stabilizing cover 82 a attachedalong cutout width 20. FIG. 8B is a perspective view of second tube 1 bafter the second step of a method of the present invention withstabilizing covers 82 c and 82 d, each attached along opposite sides ofcutout 12. FIG. 8C is a perspective view of the resulting joint 60 withstabilizing covers 82 a and 82 b shown, when tubes 1 a and 1 b withequal external diameters are joined orthogonally using a method of thesubject invention.

Given the fact that cutout depth 23 of each tube 1 a and 1 b are halfthe length of exterior diameters 15, meaning that cutouts 12 cut tubes 1a and 1 b half-way through, each cover 82 a, 82 b, 82 c, and 82 d mustcover an area that is a half-circle with a diameter equal to theexterior diameter 15.

FIGS. 9A and 9B are two perspective views of stabilizing cover 82 a,which is one of four identical stabilizing covers of a preferredembodiment. Referring to FIGS. 9A and 9B, stabilizing cover 82 a is athree-sided, three-dimensional object bounded by a first side 90 (shownin FIG. 9A), a second side 95 (shown in FIGS. 9A and 9B), and a thirdside 99 (shown in FIG. 9B).

As shown in FIG. 9A, first side 90 is a semicircle with a diameter equalto exterior diameter 15 with a marginal thickness 91.

As shown in FIGS. 9A and 9B, second side 95 has a curved surface 96 andthree edges 97 (shown in FIGS. 9A and 9B), 98 (shown in FIGS. 9A and9B), and 98′ (shown in FIG. 9B). When the exterior diameters of tubes 1a and 1 b are equal, curved surface 96 (shown in FIGS. 9A and 9B) iscongruent to the curvature of exterior surface of tubes 1 a and 1 b. Thelength of edge 97 is equal to the arc length of first side 90, or halfthe circumference of a circle with a diameter equal to exterior diameter15. Edges 98 and 98′ are curved and identical in length, such thedistance from the point 100 (shown in FIGS. 9A and 9B) where edges 98and 98′ meet and the center of the length of edge 96 is equal toone-half exterior diameter 15. As shown in FIG. 9B, third side 99 is acurved surface that has the same curvature as the external surface oftubes 1 a and 1 b and is sized to form a closed volume with first side90 and second side 95 when sides 90 and 95 abut at a right angle.

In the preferred embodiment of the method of the subject invention, twooptional stabilizing covers can be arranged on each side cutout 12 ofeach tube 1 a and 1 b. Referring to FIG. 8B stabilizing covers 82 c and82 d are arranged one on each side of cutout 12 such that flat side ofthe semicircle of first side 90 of each stabilizing cover isperpendicular to central axis of tube 1 b and aligns with the bottomedge on each side of cutout 12 and the exterior surface of second tube 1b abuts the surface of third side 99. The surface of third side 99 ofeach of the stabilizing covers 82 c and 82 d are attached to theexterior surface of second tube 1 b using epoxy, glue, adhesive, orother means of affixing two objects together.

When stabilizing covers 82 a, 82 b, 82 c, and 82 d are used, cutoutwidths 20 (shown in FIG. 8A) on both tubes 1 a and 1 b should beincreased by an amount equal to twice thickness 91 to accommodatestabilizing covers 82 a, 82 b, 82 c, and 82 d.

Two stabilizing covers are arranged and affixed to each tube 1 a and 1 bsuch that the flat edge of the semicircle of first side 90 of eachstabilizing cover aligns on each side of the cutout widths 20 of eachtube 1 a and 1 b and the exterior surface of the tube abuts the surfaceof the third side 99 of the stabilizing cover. The surface of third side99 of each of the stabilizing covers are attached to the exterior ortube using epoxy, glue, adhesive, or other means of affixing two objectstogether. As shown in FIG. 8A, the flat edge of the semicircle of firstside 90 of stabilizing cover 82 a is aligned with the edge of cutoutwidth 20 of tube 1 a. FIG. 8B is a perspective view of second tube 1 bwith stabilizing covers 82 c and 82 d at each side of cutout 12 of tube1 b.

The invention can be further refined by inserting two optionalstabilizing, circular discs into each tube 1 a and tube 1 b aftercompletion of the second step of method of the subject invention. Thecircular discs add additional strength to tubes 1 a and 1 b where theyhave been modified to create cutouts 12 on tubes 1 a and 1 b, andprovide a means to keep water from entering tubes 1 a and 1 b from joint60, or from entering the joint 60 from tubes 1 a and 1 b, making theresulting joint 60 waterproof.

Referring to FIG. 10, which is a perspective view of disc 105, one ofthe four identical right circular cylinder discs. Each disc 105 has twocircular bases 103 and 103′ with a radius equal to one-half interiordiameter 13 and a curved surface 109. The length 107 of curved surface109, which is the distance between circular base 103 and 103′, can vary.In a preferred embodiment, length 107 is equal to the thickness of tubes1 a and 1 b.

Disc 105 is inserted into tube 1 a at exposed half-circular crosssection 17 a on one side of cutout 12 such that the central axis of disc105 aligns with the central axis 7 (shown in FIG. 1) of first tube 1 a.When inserted in the proper position, the curved surface 109 should abutwith the interior surface of tube 1 a and circular base 103 should beflush with exposed circular cross section 17 a.

Another disc 105 is inserted into tube 1 a at exposed half-circularcross section 17 b on the opposite side of cutout 12 on tube 1 a suchthat the central axis of disc 105 aligns with the central axis 7 (shownin FIG. 1) of first tube 1 a and circular base 103 of disc 105 will beflush with exposed half-circular cross section 17 b. When inserted,curved surface 109 should abut with the interior surface of first tube 1a along exposed half-circular cross section 17 b. FIG. 5B is aperspective view of disc 105 properly inserted and positioned in firsttube 1 a with circular base 103 flush with exposed half-circular crosssection 17 b.

Similarly, two additional discs 105 can be inserted into second tube 1 bat exposed half-circular cross-sections 17 a and 17 b on each side ofcutout 12 of tube 1 b such that the central axis of each disc 105 alignswith central axis of second tube 1 b. When inserted, curved surface 109of disc 105 should abut with the interior surface of second tube 1 balong each side of cutout 12 and circular base 103 of each disc 105 willbe flush with exposed half-circular cross sections 17 a and 17 b ofsecond tube 1 b.

The four discs 105 can be attached to tubes 1 a and 1 b using epoxy,glue, adhesive, or any other means for affixing objects together. Eachdisc 105 can be fabricated using one or more methods known in the art.For example, a hole saw mounted in a drill press can be used to cut eachdisc 105 from a rigid material, such as carbon fiber, or each disc 105can be made with a 3D printer.

In the preferred embodiment where four discs 105 and two halves 40 a and40 b (shown in FIG. 4B) are utilized, a lacuna is created in each tube 1a and 1 b between the curved surface of half 40 a or 40 b and circularbase 103 of one of the four discs 105. In one embodiment of the methodof the subject invention, these lacunas can be filled with epoxy, glue,adhesive, or any other means for affixing objects together.

In another embodiment of the method for the subject invention, insteadof tubes 1 a and 1 b having exterior diameters 15 of the same length,two tubes 1 a and 1 b that are selected in the first step of the methodof the subject invention will have exterior diameters 15 a and 15 b thatdiffer (the result of differing wall thicknesses of tubes 1 a and 1 b).

When exterior diameter 15 a of tube 1 a and exterior diameter 15 b oftube 1 b differ in size, instead of cutouts 12 that are equal indimension on both tubes 1 a and 1 b, the cutouts 12 a and 12 b thatmodify tubes 1 a and 1 b in the second step of the subject inventionwill differ in dimension. The width on the cutout of the smaller tubewill be the length of the exterior diameter of the larger tube and thewidth of the cutout on the larger tube would be length of the exteriordiameter of the smaller tube.

Referring to FIGS. 11A and 11B, identical and identically acting partscarry the same reference numerals as in FIG. 1. In the preferredembodiment shown in FIGS. 11A and 11B, first tube 1 a has a smallerexterior diameter 15 a than exterior diameter 15 b of second tube 1 b.FIG. 11A is a perspective view of tube 1 a modified with cutout 12 a toaccept tube 1 b with a larger exterior diameter than exterior diameter15 a. FIG. 11B is a perspective view of tube 1 b modified with cutout 12b to accept tube 1 a with a smaller exterior diameter than exteriordiameter 15 b. As shown in FIGS. 11A and 11B, once tubes 1 a and 1 b aremodified with cutouts 12 a and 12 b, each cutout 12 a and 12 b createstwo exposed half-circular cross sections 17 a and 17 b that areperpendicular to central axis 7 at either side of cutout 12 a and 12 b.

The size of cutouts 12 a and 12 b will depend on exterior diameters 15 aand 15 b of the tubes being used. From the side view, as shown in FIGS.12A and 12B, cutouts 12 a and 12 b each have a U-shaped side-profilethat have a cutout width 20 a and 20 b, respectively, and cutout depth23 a and 23 b, respectively.

Referring to FIG. 12A, the length of cutout width 20 a of first tube 1 ais equal to the length of exterior diameter 15 b of second tube 1 b andcutout depth 23 a is half the length of exterior diameter 15 a. FIG. 12Bis a side view of tube 1 b shown in FIG. 11B after the second step of amethod of the subject invention. The length of cutout width 20 b ofsecond tube 1 b is equal to the length of exterior diameter 15 a of tube1 a and cutout depth 23 b is equal to half the length of exteriordiameter 15 b.

When tubes 1 a and 1 b have exterior diameters 15 a and 15 b ofdiffering length, the use of four optional stabilizing covers 82 a, 82b, 82 c, and 82 d described above would leave an obvious gap becausewhen tubes 1 a and 1 b are orthogonally arranged with cutouts 12 oftubes 1 a and 1 b facing one another, the tube with the smaller exteriordiameter would not fill the cutout of the tube with the larger exteriordiameter, since the cutout depth of the larger tube would equal to onehalf the exterior diameter of the larger tube. Therefore, in anotherpreferred embodiment, the use of two stabilizing covers 82 a and 82 band one cutout bridge 113 can be used instead for four stabilizingcovers described above. Stabilizing covers 82 a and 82 b will be placedon the tube with the larger exterior diameter, and cutout bridge 113will be placed on the tube with the smaller exterior diameter.

When cutout bridge 113 is used, the width of the cutout on the largertube should be cut to the exterior diameter of the smaller tube plus asmall margin to accommodate the bottom edges of the cutout bridge. Thewidth of the cutout on the smaller tube should be cut to the width ofthe outer diameter of the larger tube, plus a small margin toaccommodate the combined thicknesses 91 of the bottom edges of the twostabilizing covers.

In the preferred embodiment shown in FIGS. 11A and 11B, where first tube1 a has a smaller exterior diameter 15 a than the exterior diameter 15 bof second tube 1 b, stabilizing covers 82 a and 82 b would be affixed tosecond tube 1 b. The semicircular shape of first side 90 of stabilizingcovers 82 a and 82 b would have diameter equal to the length of exteriordiameter 15 a, which is the exterior diameter of the smaller tube. Thecurved surface of third side 99 of each stabilizing cover 82 a and 82 bwould have the same curvature as the external surface of first tube 1 a.

FIG. 13A is a perspective view of optional cutout bridge 113 for joiningtubes 1 a and 1 b of varying external diameters. Cutout bridge 113 is athree-dimensional shape defined as a semicircular cylinder 114 of radiusequal to one-half the exterior diameter of the tube with the largerexterior diameter and a length marginally longer than the exteriordiameter of the smaller tube, less the volume of a semicircular cylinder116 of diameter equal to the exterior diameter smaller tube and a lengthequal to exterior diameter of the larger tube arranged such that thecylindrical axes of semicircular cylinders 114 and 116 intersectorthogonally. Because the length of semicircular cylinder 114 ismarginally longer than the exterior diameter of the smaller tube, thereis a margin 115 a and 115 b on each side of semicircular cylinder 116.

The concave surface 117 formed by the removal of the volume ofsemicircular cylinder 116 from semicircular cylinder 114 is affixed tothe exterior surface of the tube with the smaller exterior diameter suchthat the axis of semicircular cylinder 116 aligns with central axis 7 ofthe tube with the smaller exterior diameter and the straight edge of thesemicircular faces of semicircular cylinder 114 align and abut with edgeof cutout width of the tube with the smaller exterior diameter.

FIG. 13B is a perspective view of cutout bridge 113 affixed to theexterior surface of tube 1 a, which exterior diameter 15 a (shown inFIG. 11A) is smaller in length than the exterior diameter 15 b on tube 1b (shown in FIG. 11B). Cutout bridge 113 is affixed to the exteriorsurface of tube 1 a such that the axis of semicircular cylinder 116aligns with the axis of tube 1 a. The straight edge of semicircularcylinder 114 aligns and abuts with the cutout width of tube 1 a. In apreferred method of attaching the cutout bridge to the smaller tube 1 a,tubes 1 a and 1 b should be orthogonally positioned to form joint 60.Cutout bridge 113 is then positioned and attached over the top of thesmaller tube 1 a to ensure cutout bridge 113 has been correctly made andpositioned so that it covers the lateral openings of the cutout in thelarger tube 1 b, making a close fit.

FIGS. 14A and 14B are perspective views of both sides of the resultingjoint 60 created by a method of the subject invention with the optionalcutout bridge 113 and two stabilizing covers 82 a and 82 b utilized. Inthe perspective view in FIG. 14A, the resulting joint is covered bycutout bridge 113 affixed to tube 1 a, which has a smaller exteriordiameter than tube 1 b. The perspective view in FIG. 14B shows twostabilizing covers 82 a and 82 b affixed to tube 1 b, which has thelarger exterior diameter than tube 1 a.

For the fixed version of joint 60, epoxy, glue, adhesive, or other canbe liberally applied to the bases of the notched bridge and lateral“openings” of the cutout of the larger tube, edges of the cutout, andall interfacing surfaces of the internal parts of the Steinmetz solid.Straps may be used in lieu of a clamp until the adhesive has fullyhardened, and then straps may be removed.

When exterior diameters of tubes 1 a and 1 b are unequal, two identicalstepped stoppers 120 a can be used in place of circular discs in thetube with the smaller external diameter. FIG. 15A is a perspective viewof stepped stopper 120 a. As shown in FIG. 15A, stepped stopper 120 a isa circular disc 121 with a diameter equal to internal diameters of thetwo tubes and a thickness 124 joined axially with a semicircular disc135 with a diameter equal to internal diameter of the tubes and athickness 126. Thickness 126 is equal to one-half the tube wall of thetube with the larger exterior diameter. In a preferred embodiment,thickness 124 is equal to the thickness of the tube wall of the tubewith the smaller exterior diameter, however thickness 124 can vary.

FIG. 15B is a perspective view of stepped stopper 120 a properlyinserted and positioned in first tube 1 a with circular disc 121 flushwith exposed half-circular cross section 17 a. Identical and identicallyacting parts carry the same reference numerals as in FIG. 15A. Referringto FIG. 15B, a preferred method of the subject invention uses themodified tubes shown in FIG. 11A, with first tube 1 a having a smallerexterior diameter 15 a than the exterior diameter 15 b of second tube 1b. After tube 1 a is modified with second cutout 12 a, two steppedstoppers 120 a are affixed to the interior surface of tube 1 a at thetwo exposed half-circular cross sections 17 a and 17 b created by cutout12 a such that the axes of circular disc 121 of each stepped stopper 120a align with the center axis 7 of first tube 1 a (shown in FIG. 11A).

After second tube 1 b is modified with cutout 12 b, two circular discswith diameter equal to interior diameters 13 are affixed to the insidesurface of second tube 1 b at the two exposed circular cross sections 17a and 17 b of second tube 1 b, as described above, such that the axes ofeach disc 105 are aligned with central axis 7 of second tube 1 b (shownin FIG. 11B).

The subject invention also comprises a kit for joining cylindrical tubesto form strong orthogonal joints. The kit would include one or more ofthe following elements: a tool for producing cuts in said cylindricaltubes of specified width and depth as described above including, by wayof example, knives, saws and cutters, manually operated and powered; aSteinmetz solid connector having shape defined by the volume ofintersection of two cylindrical volumes of equal diameter withorthogonally intersecting cylindrical axes; and adhesive(s) forattaching said cylindrical tubes and connector.

Additionally, or optionally, the kit could further comprise one or moreof the following auxiliary parts: (1) straps or other means for areleasably securing the joint as described above, (2) four circulardiscs as described above each with a diameter equal to the internaldiameter of the cylindrical tubes, (3) four stabilizing covers asdescribed above, (4) two stabilizing covers and a cutout bridge asdescribed above, and/or (5) two circular discs and two stepped stoppersas described above.

SUMMARY AND SCOPE

The above-described invention could have a number of applications,including, but not limited to, creating modular wings and lightweightfurniture and camping equipment.

With respect to modular wings, joints in current wing structures such aspower generating wind turbines, wingsails, and aircraft wings, arepermanently fixed and cannot be disassembled, which greatly limits thepotential use of wings in many important areas. The subject inventioncould be applied to each of these types of permanently fixed wings tocreate modular wings.

Wind driven turbines that produce electricity for the power grids aroundthe world have become a multi-billion-dollar industry, and—perhaps mostimportantly—provide hope that we may save earth from furthercarbon-induced climate change. The three long, thin carbon-fiber bladesin use on today's wind turbines have the advantages of being fairlylightweight, low maintenance and easy to clean. They are, on the otherhand, far less efficient in capturing wind energy than wings that moreclosely resemble aircraft wings. This is true because the principles ofaerodynamics that produce lift for airplanes are the same as those thatproduce thrust for wind turbines. Wind turbine blades resemblingaircraft wings could be made using modern fabrics like Kevlar® (widelyused by sailboats) stretched across a carbon-fiber frame made using thesubject invention. The subject invention would make the blades modularso that they could be easily removed, cleaned, serviced and placed backinto use. Such an application would solve the weight and cleaning issuewhile providing a greater power producing output that would offset thecleaning and maintenance costs.

A wingsail is a variable-camber aerodynamic structure that is fitted toa marine vessel in place of conventional sails. Wingsails are analogousto airplane wings, except that they are designed to provide lift oneither side to accommodate being on either tack. Whereas wings adjustcamber with flaps, wingsails adjust camber with a flexible or jointedstructure (for hard wingsails). Wingsails are typically mounted on anunstayed spar—often made of carbon fiber for lightness and strength. Thegeometry of wingsails provides more lift, and a better lift-to-dragratio, than traditional sails. Wingsails are more complex and expensivethan conventional sails. None of today's wingsails are modular. Withtoday's non-modular wingsails, the Kevlar® fabric that covers thecarbon-fiber frames are glued (epoxied) to the ribs. This presentsproblems that only a team of experienced Kevlar® and carbon-fiberfabricators and construction experts can handle. And these fabricatorsand experts need to be on site at every race or other sailing outing.Applying the subject invention to create a modular wingsail would solvemany problems that non-modularity presents, including issues with fabricstretching and crashes.

First, all fabrics stretch, even the latest Dacron and Kevlar® weavesspecifically designed not to stretch, over time will stretch. A modularwing would have its fabric spread across its frame and fastened withcleated ropes or ties or any number of methods, and the surfaces of thefabric that abutted the ribs would use attached velcro strips to securethe fabric to the ribs (instead of glue). Maintenance of a wings ailwould include pulling the fabric-covering loose from its velcroattachment, repositioning it, smoothing out any wrinkles, cinching itdown, and then pressing the abutting fabric down onto the ribs' velcrostrips again.

Second, some boats using wingsails are topping 50 mph. They are flyingabove the water on foils, and while this sort of sailing is relativelynew, and a great deal of effort has been made to reduce the number ofcrashes, crashes remain a regular occurrence, and they frequentlyinvolve structural damage to the wing's frame and occasionally tears inthe wing's fabric covering. Torn fabric is easily repaired. Broken ribsare not. If wingsails were in wide use, the availability of spares forevery piece of a wing's frame would be easily available and relativelyinexpensive.

The subject invention could also be used to improve aircraft wings thatare covered with fabric like the Bellancas. Bellancas in their day brokeall the records for Atlantic crossings, first aircraft in inter-islandair service in Hawaii, speed records, etc. Designed by an Italiangenius, and built by hand, almost everyone who loved flying wanted aBellanca. There may be a market if the aeronautical specifications ofthe external surfaces of the Bellanca Super Viking could be used toreinvent that aircraft using the same engine and avionics, but replacingthe wood and heavily doped and painted cloth with carbon-fiber modularwing structures covered with Kevlar® fabric.

The subject invention could also be used to improve wind tunnels,exhaust fans, and large blowers of every type. Similar to the describedimprovements of wings discussed above, the same could be applied tocreate modular blades for wind tunnels, exhaust fans and large blowers.However, unlike wingsails, whose airfoil shape is symmetrical to providelift on either tack, wind turbines, blowers, and fans would have anasymmetrical shape appropriate to function.

With respect to lightweight furniture and camping equipment, the subjectinvention could be used to create an improved portable chair. Portablechairs generally come in only two or three varieties. None of them aresomething a person would pack in their luggage for travel on anairplane, primarily because they are too bulky and too cheap. Foldablechairs, and long-pole deep bag-type chairs do not fit into a normalsuitcase either, or take up too much room. Given the fact that suchchairs generally are cheaply made with inexpensive materials, they windup in landfills or fill the bottom of lakes and lagoons, clog waterways,and trash the landscape. The subject invention can be used to create ahigh end, comfortable, elegant looking portable chair that travelerswould keep in their luggage when not in use. For example, such a chaircould have an orthogonally joined, and strapped together pair ofcarbon-fiber tubes approximately fourteen inches in length to form thebase of such a chair.

The subject invention could also be used to improve tents and otherportable living quarters. There is a global need for quality portableliving quarters, beyond simple tents. Portable chairs, and similarlyconstructed platforms for air mattresses, quickly constructed andcollapsed tables and other furniture, enclosed living quarters with roomto stand up, could all be made using the subject invention.

Although the description above contains many specificities, these shouldnot be construed as limiting the scope of the invention but merelyproviding illustrations of some of the presently preferred embodimentsof this invention. Thus, the scope of the invention should be determinedby the appended claims and their legal equivalents, rather than by theexamples given.

For example, use of the term “epoxy” or “epoxied” is not intended toimply that Epoxy—and only Epoxy—is required for these embodiments. Forall purposes in this application, any “adhesive,” “glue,” means for“gluing”, “welding”, and/or “attaching” known to the art can be used.

Also, whereas some embodiments describe bisected or quartered Steinmetzsolids, the process for making such connectors need not involvebisection or quartering but, instead, such connector pieces may beformed individually to exhibit the size and shape of a bisected orquartered integral Steinmetz solid.

Additionally, although the descriptions above specify carbon fibermaterial, it is anticipated that any rigid material may be substitutedfor the carbon fiber material described.

The terms “cylinder”, “pipe”, and/or “tube” may be used interchangeably,and will always mean a right circular cylinder, i.e., a cylinder withthe bases circular and with the axis joining the two centers of thebases perpendicular to the planes of the two bases. It is anticipatedthat applications for Steinmetz solid technology will involve carbonfiber tubing, hence the term “tube” will replace the term “cylinder”and/or “pipe” for the most part.

Unless otherwise specified, the joints described herein are orthogonal,i.e., the two cylinders/tubes intersect at right angles.

The Steinmetz solid joint's intended use is structural, to bedistinguished from orthogonally joined pipes used to convey fluids(water, gas, oil, sewage, packages via pneumatic tubes, etc.). Unlikethese, Steinmetz solid technology joins together two tubes orthogonallyprimarily for structural applications.

Although some embodiments are shown to include certain features, it isspecifically contemplated that any feature disclosed herein may be usedtogether or in combination with any other feature on any embodiment ofthe invention. It is also contemplated that any feature may bespecifically excluded from any embodiment of the invention.

As used herein, the following terms and variations thereof have themeanings given below, unless a different meaning is clearly intended bythe context in which such term is used. “A,” “an”, and “the” and similarreferents used herein are to be construed to cover both the singular andthe plural unless their usage in context indicates otherwise.

“Comprise” and variations of the term, such as “comprising” and“comprises,” are not intended to exclude other additives, components,integers, or steps.

Unless otherwise indicated, all numbers, dimensions, materials, and soforth used in the specification and claims are to be understood as beingexamples and not limitations, and in any event, should not be construedas an attempt to limit the application of the doctrine of equivalents tothe scope of the claims.

All methods described herein can be performed in any suitable orderunless otherwise indicated herein or otherwise clearly contradicted bycontext. The use of any and all examples, or exemplary language (e.g.,“such as”) provided herein is intended merely to better illuminate theinvention and does not pose a limitation on the scope of any claim. Nolanguage in the specification should be construed as indicating anynon-claimed element essential to the practice of the invention.

Certain embodiments are described herein, including the best mode knownto the inventor for carrying out the invention. Of course, variations onthese described embodiments will become apparent to those of ordinaryskill in the art upon reading the foregoing description. The inventorexpects skilled artisans to employ such variations as appropriate, andthe inventors intend for the invention to be practiced otherwise thanspecifically described herein.

Accordingly, the claims include all modifications and equivalents of thesubject matter recited in the claims as permitted by applicable law.Moreover, any combination of the above-described elements in allpossible variations thereof is contemplated unless otherwise indicatedherein or otherwise clearly contradicted by context. The inventionshould therefore not be limited by the above-described embodiment,method, and examples, but shall be deemed to include all embodiments,methods, and equivalents within the scope and spirit of the invention asclaimed.

In closing, it is to be understood that the embodiments disclosed hereinare illustrative of the principles of the claims. Other modificationsthat may be employed are within the scope of the claims. Thus, by way ofexample, but not of limitation, alternative embodiments may be utilizedin accordance with the teachings herein. Accordingly, the claims are notlimited to embodiments precisely as shown and described.

I claim:
 1. A kit for joining cylindrical tubes to form strongorthogonal joints, comprising: a. a Steinmetz solid connector having ashape defined by the volume of intersection of the two cylindricalvolumes of equal internal diameter joined orthogonally; and b. adhesivemeans for securing said connector within said cylindrical tubes.
 2. Thekit of claim 1 further comprising one or more tools for modifyingcylindrical tubes to demonstrate cutouts of specified width and depth atthe location of an intended joint.
 3. The kit of claim 1, wherein saidconnector comprises a single piece.
 4. The kit of claim 1 wherein saidSteinmetz solid connector is comprised of a plurality of pieces.
 5. Thekit of claim 4 wherein said connector is comprised of two identicalhalf-connectors each exhibiting a shape obtained by bisecting theSteinmetz solid between one set of opposed corners to form halfconnectors each having a curved surface and a planar surface.
 6. The kitof claim 5 wherein the adhesive means for securing said connector withinsaid cylindrical tubes is one or more straps for lashing around theresulting joint.
 7. The kit of claim 4 wherein said connector comprisesfour identical quarter-connectors each exhibiting a shape obtained bybisecting the Steinmetz solid between both sets of opposed corners toform quarter-connectors each having a curved surface and two planarsurfaces.
 8. The kit of claim 7 wherein the adhesive means for securingsaid connector within said cylindrical tubes is one or more straps forlashing around the resulting joint.
 9. The kit of claim 1 wherein saidtubes are of equal external diameter and further comprising fourstabilizing covers, each having a shape defined by the volume bounded bythe following three surfaces: the first, a planar surface congruent to asemicircle of diameter equal to the external diameter of said tubes, thesecond, a curved surface congruent to one octant of the surface of saidSteinmetz solid of which the long uncurved side abuts the first saidsurface at its diameter, and the third, a section of the surface of acylinder of diameter equal to the external diameter of said tubes sizedto form a closed volume with the first and second said surfaces andaligned so that the third surface abuts the first said surface at aright angle.
 10. The kit of claim 1 wherein said tubes are not of equalexternal diameter and further comprising two stabilizing covers, eachhaving a shape defined by the volume bounded by the following threesurfaces: the first, a planar surface congruent to a semicircle ofdiameter equal to the external diameter of the larger of said tubes, thesecond, a curved surface congruent to one octant of the surface of saidSteinmetz solid of which the long uncurved side abuts the first saidsurface at its diameter, and the third, a section of the surface of acylinder of diameter equal to the external diameter of the larger ofsaid tubes sized to form a closed volume with the first and second saidsurfaces and aligned so that the third surface abuts the first saidsurface at a right angle.
 11. The kit of claim 1 wherein said tubes haveequal external diameters and further comprising four circular discs ofdiameter equal to the internal diameter of said tubes and thicknessequal to the tube thickness defined by the distance between the innerand outer tube diameters.
 12. The kit of claim 1 wherein said tubes haveunequal external diameters and further comprising: a. two circular discseach of diameter equal to the internal diameter of said tubes andthickness equal to the thickness of the larger of said tubes defined bythe distance between the inner and outer tube diameter; and b. twostepped stoppers each of volume equal to a circular disc of diameterequal to the internal diameter of said tubes and thickness equal to thethickness of the smaller of said tubes defined by the distance betweenthe inner and outer tube diameters joined axially with a bisectedcircular disc of diameter equal to the internal diameter of said tubesand thickness equal to the thickness of the larger of said tubes.
 13. Akit for joining cylindrical tubes of equal internal diameter to formstrong orthogonal joints, comprising: a. a bicylinder Steinmetz solidconnector having a shape defined by the volume of intersection of thehollow regions of said tubes when said tubes are joined orthogonally;and b. adhesive means for securing said connector within saidcylindrical tubes at the location of the intended joint.
 14. The kit ofclaim 13, further comprising a one or more tools for modifying each saidtube to demonstrate a cutout at the location of the intended joint toexpose a section of the inside surface of said tube, said cutout on thefirst tube having a depth equal to one half the external diameter ofsaid first tube and a width equal to the external diameter of the secondsaid tube, and said cutout on said second tube having a depth equal toone half the external diameter of said second tube and a width equal tothe external diameter of said first said tube.
 15. The kit of claim 13,wherein said connector comprises a single piece.
 16. The kit of claim 13wherein said Steinmetz solid connector is comprised of a plurality ofpieces.
 17. The kit of claim 16 wherein said connector is comprised oftwo identical half-connectors each exhibiting a shape obtained bybisecting the Steinmetz solid between one set of opposed corners to formhalf connectors each having a curved surface and a planar surface. 18.The kit of claim 16 wherein said connector comprises four identicalquarter-connectors each exhibiting a shape obtained by bisecting theSteinmetz solid between both sets of opposed corners to formquarter-connectors each having a curved surface and two planar surfaces.19. The kit of claim 13 wherein said tubes are of equal externaldiameter and further comprising four stabilizing covers, each having ashape defined by the volume bounded by the following three surfaces: thefirst, a planar surface congruent to a semicircle of diameter equal tothe external diameter of said tubes, the second, a curved surfacecongruent to one octant of the surface of said Steinmetz solid of whichthe long uncurved side abuts the first said surface at its diameter, andthe third, a section of the surface of a cylinder of diameter equal tothe external diameter of said tubes sized to form a closed volume withthe first and second said surfaces and aligned so that the third surfaceabuts the first said surface at a right angle.
 20. The kit of claim 13wherein said tubes are not of equal external diameter and furthercomprising two stabilizing covers, each having a shape defined by thevolume bounded by the following three surfaces: the first, a planarsurface congruent to a semicircle of diameter equal to the externaldiameter of the larger of said tubes, the second, a curved surfacecongruent to one octant of the surface of said Steinmetz solid of whichthe long uncurved side abuts the first said surface at its diameter, andthe third, a section of the surface of a cylinder of diameter equal tothe external diameter of the larger of said tubes sized to form a closedvolume with the first and second said surfaces and aligned so that thethird surface abuts the first said surface at a right angle.
 21. The kitof claim 13 wherein said tubes have equal external diameters and furthercomprising four circular discs of diameter equal to the internaldiameter of said tubes and thickness equal to the tube thickness definedby the distance between the inner and outer tube diameters.
 22. The kitof claim 13 wherein said tubes have unequal external diameters andfurther comprising: a. two circular discs each of diameter equal to theinternal diameter of said tubes and thickness equal to the thickness ofthe larger of said tubes defined by the distance between the inner andouter tube diameter; and b. two stepped stoppers each of volume equal toa circular disc of diameter equal to the internal diameter of said tubesand thickness equal to the thickness of the smaller of said tubesdefined by the distance between the inner and outer tube diametersjoined axially with a bisected circular disc of diameter equal to theinternal diameter of said tubes and thickness equal to the thickness ofthe larger of said tubes.